You have gotten great answers so far. Also, I suggest for the kids, pack a small bag of "new" toys for them so if they get bored or start to fuss you can pull one item out at a time to entertain. I usually just go to Wal-Mart or the dollar store and find several inexpensive new things (or borrow toys from a friend). I always bring snacks and a DVD player also so I usually don't have to get everything out at once and have some left for the return flight. I just bring one thing out at a time as needed and each item lasts awhile. This has saved many meltdowns! Even for other kids around us. I've seen people fly with no snacks, toys, or anything for their little ones and they have had meltdowns so we've offered to share books, toys, etc. to help not drive everybody else crazy from their screaming. My son is 5 and has flown with me about 20 times since he was 9 months and this has always been a lifesaver for me.
When he was less than 2 and didn't require a carseat on the plane, I always checked that so I didn't have to deal with it. You can check the carseat and stroller at the gate, carry any snacks, and the sealed formula is fine. You can take a bottle of formula/milk through security, but not juice. You can always buy that once you get through or get it on the plane. Also, make sure if you have an liquid medicines or jars of baby food that you put those in the quart size clear baggie for security. Baby food counts as a liquid/gel as I found out the hard way once and had to have the entire diaper bag searched after not knowing that!
Sit by other kids if you fly Southwest and have a choice of seats. That sometimes helps, too:-) They'll help entertain each other.
Good luck!